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  2. Volume of the Sphere

Volume of the Sphere

016 Radius of the sphere circumscribing a regular triangular pyramid

Example 016
Find the area of the surface and the volume of the sphere circumscribed about a regular tetrahedron of edge 25 cm. See Figure 015.
 

Sphere circumscribed about a regular tetrahedron

 

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015 Two unequal balls inside the cylinder

Example 015
Two balls, one 15 cm in diameter and the other 10 cm in diameter, are placed in a cylindrical jar 20 cm in diameter, as shown in Figure 014. Find the volume of water necessary to cover them.
 

016-balls-inside-cylinder.gif

 

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014 Water poured into a jar of marbles

Example 014
A boy who had discovered that 20 mm marbles fitted snugly into the bottom of a cylindrical jar, dropped in a fourth on top of the three and poured water enough into the jar to just cover them. How much water did he use?
 

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013 Insciribed and circumscribed sphere about a cube - volume comparison

Example 013
Compare the volume of a sphere inscribed in a cube with volume of the sphere that circumscribes the cube.
 

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012 Sphere circumscribed about a right circular cylinder

Example 012
Find the volume and total area of the sphere which circumscribes a cylinder of revolution whose altitude and diameter are each 6 inches.
 

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007 - 008 Volume and surface area of earth and balloon

Example 007
A spherical balloon is inflated so that so that its diameter is 12 m. Find the surface area of the balloon’s covering and the volume of the gas.
 

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005 Weight of ivory billiard balls

Example 005
A cubic foot of ivory weighs 114 lb. Find the weight of 1000 ivory billiard balls 2½ inch in diameter.
 

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003 Weight of an iron shell

Example 003
An iron ball 10 cm in diameter weighs 4 kg. Find the weight of an iron shell 5 cm thick whose external diameter is 50 cm.
 

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002 Weight of snow ball

Problem 002
Find the weight of the snowball 1.2 m in diameter if the wet compact snow of which this ball is made weighs 480 kg/m3
 

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001 Solid steel ball remolded into hollow steel ball

Problem 001
A 523.6 cm3 solid spherical steel ball was melted and remolded into a hollow steel ball so that the hollow diameter is equal to the diameter of the original steel ball. Find the thickness of the hollow steel ball.
 

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